We consider nonlinear algebraic systems resulting from numerical discretizations of nonlinear partial differential equations of diffusion type. In order to solve them, some iterative nonlinear solver, and, on each step of this solver, some iterative linear solver are used. In Part I of this work, we have developed a general abstract framework hinging on equilibrated flux reconstructions to derive stopping criteria for both iterative solvers and to control the size and distribution of the overall approximation error. In this Part II, we apply this framework to various discretization schemes like finite elements, nonconforming finite elements, discontinuous Galerkin, finite volumes, and lowest-order mixed finite elements; to different linearizations like fixed point and Newton; and to arbitrary iterative linear solvers. This leads to new guaranteed and robust a posteriori error estimates for nonlinear diffusion problems in the presence of linearization and algebraic errors. Moreover, for many discretization schemes, we improve on, or derive new, flux equilibration techniques.
